• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.349-355
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• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.27 no.1
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• pp.83-90
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• 1991

The method, which is introduced here, is an approximation derived by an application of the slender body theory, which has achieved a great success in the field of aeronautical engineering. However numerical results for wave resistance by this theory have been very disappointing. A slender body formulation for a ship in uniform forward motion si presented. It is based on the asymptotic expansion of the Kelvin source and the result is quite different from the existing slender ship theory developed by Vossers, Tuck and Maruo. It is equivalent to an approximation for the kernel function of the Neumann-Kelvin problem which assumes the linearized free surface condition but deals with the body boundary condition in its exact from. The velocity field and pressure distribution can be calculated simply by the differentiation of the two-dimensional velocity potential. A formula for the wave resistance of slender ships is also presented.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.23 no.3
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• pp.111-116
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• 1987

The accurate prediction of the ship wave resistance is very important to design ships which operate satisfactorily in a wave environment. Thus, work should continue on development and validation of methods to compute ship wave patterns and wave resistance. Research efforts to improve the prediction of ship waves and wavemaking resistance are categorized in two major areas. First is the development of higher-order theories to take account of the nonlinear effect of the free surface condition and improved analytical treatment of the body boundary condition. Second is the development of direct numerical methods aimed at solving body and free-surface boundary conditions as accurately as possible. A new formulation of the slender body theory for a ship with constant speed is developed by Maruo. It is quite different from the existing slender ship theory by Vossers, Maruo and Tuck. It may be regarded as a substitute for the Neumann-Kelvin approximation. In present work, the method of asymptotic expansion of the Kelvin source is applied to obtain a new wave resistance formulation in fluid of finite depth. It takes a simple form than existing theory.

• Journal of the Korean Data and Information Science Society
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• v.24 no.5
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• pp.999-1011
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• 2013

In this research, we propose a document recommendation method which can find documents that are relatively important to a specific document based on citation information. The key idea is parameter tuning in the Neumann kernal which is an intermediate between a measure of importance (HITS) and of relatedness (co-citation). Our method properly selects the tuning parameter ${\gamma}$ in the Neumann kernal minimizing the prediction error in future citation. We also discuss some comutational issues needed for analysing large citation data. Finally, results of analyzing patents data from the US Patent Office are given.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.23 no.3
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• pp.1-1
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• 1987

The accurate prediction of the ship wave resistance is very important to design ships which operate satisfactorily in a wave environment. Thus, work should continue on development and validation of methods to compute ship wave patterns and wave resistance. Research efforts to improve the prediction of ship waves and wavemaking resistance are categorized in two major areas. First is the development of higher-order theories to take account of the nonlinear effect of the free surface condition and improved analytical treatment of the body boundary condition. Second is the development of direct numerical methods aimed at solving body and free-surface boundary conditions as accurately as possible. A new formulation of the slender body theory for a ship with constant speed is developed by Maruo. It is quite different from the existing slender ship theory by Vossers, Maruo and Tuck. It may be regarded as a substitute for the Neumann-Kelvin approximation. In present work, the method of asymptotic expansion of the Kelvin source is applied to obtain a new wave resistance formulation in fluid of finite depth. It takes a simple form than existing theory.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.21 no.2
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• pp.131-136
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• 1985

The calculation of the resulting fluid motion is an important problem of ship hydrodynamics. For a partially immersed body the condition of constant pressure at the free surface can be linearized. The resulting linear boundary-value problem for the velocity potential is the Neumann-Kelvin problem. The two-dimensional Neumann-Kelvin problem is studied for the half-immersed circular cylinder by Ursell. Maruo introduced a slender body approach to simplify the Neumann-Kelvin problem in such a way that the integral equation which determines the singularity distribution over the hull surface can be solved by a marching procedure of step by step integration starting at bow. In the present pater for the two-dimensional Neumann-Kelvin problem, it has been suggested that any solution of the problem must have singularities in the corners between the body surface and free surface. There can be infinitely many solutions depending on the singularities in the coroners.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1255-1274
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• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.81-105
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• 2003

This paper deals with the very interesting problem about the influence of piecewise smooth boundary conditions on the distribution of the eigenvalues of the negative Laplacian in R$^3$. The asymptotic expansion of the trace of the wave operator (equation omitted) for small ｜t｜ and i=√-1, where (equation omitted) are the eigenvalues of the negative Laplacian (equation omitted) in the (x$^1$, x$^2$, x$^3$)-space, is studied for an annular vibrating membrane $\Omega$ in R$^3$together with its smooth inner boundary surface S$_1$and its smooth outer boundary surface S$_2$. In the present paper, a finite number of Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components (equation omitted)(i = 1,...,m) of S$_1$and on the piecewise smooth components (equation omitted)(i = m +1,...,n) of S$_2$such that S$_1$= (equation omitted) and S$_2$= (equation omitted) are considered. The basic problem is to extract information on the geometry of the annular vibrating membrane $\Omega$ from complete knowledge of its eigenvalues by analysing the asymptotic expansions of the spectral function (equation omitted) for small ｜t｜.